Chromosomes are carriers of genetic material and their accurate transfer from a mother cell to its two daughters during cell division is of paramount importance for life. Kinetochores are crucial for this process, as they connect chromosomes with microtubules in the mitotic spindle. Kinetochores are multi-subunit complexes that assemble on specialized chromatin domains, the centromeres, that are able to enrich nucleosomes containing the histone H3 variant centromeric protein A (CENP-A). A group of several additional CENPs, collectively known as constitutive centromere associated network (CCAN), establish the inner kinetochore, whereas a ten-subunit assembly known as the KMN network creates a microtubule-binding site in the outer kinetochore. Interactions between CENP-A and two CCAN subunits, CENP-C and CENP-N, have been previously described, but a comprehensive understanding of CCAN organization and of how it contributes to the selective recognition of CENP-A has been missing. Here we use biochemical reconstitution to unveil fundamental principles of kinetochore organization and function. We show that cooperative interactions of a seven-subunit CCAN subcomplex, the CHIKMLN complex, determine binding selectivity for CENP-A over H3-nucleosomes. The CENP-A:CHIKMLN complex binds directly to the KMN network, resulting in a 21-subunit complex that forms a minimal high-affinity linkage between CENP-A nucleosomes and microtubules in vitro. This structural module is related to fungal point kinetochores, which bind a single microtubule. Its convolution with multiple CENP-A proteins may give rise to the regional kinetochores of higher eukaryotes, which bind multiple microtubules. Biochemical reconstitution paves the way for mechanistic and quantitative analyses of kinetochores.